Quantitative limits to quantum correlations in many-body systems: a signature of classical objectivity*

We quantify how much information about a quantum system can be recorded in its environment, by establishing quantitative limits to bipartite quantum correlations in many-body systems. In particular, bounds on quantum discord imply that independent observers that monitor environment fragments inevitably eavesdrop only classical information about the system, i.e. information about a pointer observable. The result validates the core idea of Quantum Darwinism: classical objectivity is not accidental, but rather a compelling feature of quantum theory. We also recast the information-theoretic signature of classical objectivity in analytical form by means of the conditional mutual information. This result enables one to monitor without hard numerical optimizations when objective reality emerges from the quantum substrate.